* How, as economist Walter Heller framed the question, to challenge Reagan economic policies without taking the risk that an upward surge in the economy next year might, temporarily at least, give the impression that Reagan was right and the Democrats were wrong?

* How, as New York Mayor Edward Koch pointed out, does the party reach out to the great mainstream of US voters without pulling away from some of the liberal causes that many of those voters can't abide?

A few days ago Democratic national chairman Charles T. Manatt, at a breakfast meeting with reporters, said that the party would, by its mid-term gathering next year, come up with a program for the 1982 and 1984 elections.

But, beyond saying that it would be a program that avoided ''me-tooism'' and harking back to the Democratic past, Mr. Manatt was able to offer few specific guidelines as to what the party's positions might be.

Thus, the Democrats still seem to be struggling with something of an identity crisis.

There also seems to be a strong vein of conservatism running through party circles. Even though most Democrats from the North don't like to be described as conservatives, many of them are today talking about the need to cut back on spending and make programs more efficient - and, in the process, sounding much more like their traditionally more conservative Southern counterparts.

But Northern liberals still tend to want to hold the line on cuts in social programs and make the slashes elsewhere, particularly in defense.

Democratic political leaders continue to report, from all geographical regions, that the President remains very popular - despite indications that a growing number of people are questioning the way he is handling his job.

Thus, Democrats are saddled with a persistent problem: how to oppose Reagan the President without antagonizing millions of Americans who continue to like Reagan the man.